Part 18 (1/2)

(_f_) The progression of the apses (with an error of one-half).

(_g_) The inequality of apogee, previously unknown.

(_h_) The inequality of nodes, previously unknown.

8. Each planet is attracted not only by the sun but by the other planets, hence their orbits are slightly affected by each other. Newton began the theory of planetary perturbations.

9. He recognized the comets as members of the solar system, obedient to the same law of gravity and moving in very elongated ellipses; so their return could be predicted (_e.g._ Halley's comet).

10. Applying the idea of centrifugal force to the earth considered as a rotating body, he perceived that it could not be a true sphere, and calculated its oblateness, obtaining 28 miles greater equatorial than polar diameter.

11. Conversely, from the observed shape of Jupiter, or any planet, the length of its day could be estimated.

12. The so-calculated shape of the earth, in combination with centrifugal force, causes the weight of bodies to vary with lat.i.tude; and Newton calculated the amount of this variation. 194 lbs. at pole balance 195 lbs. at equator.

13. A h.o.m.ogeneous sphere attracts as if its ma.s.s were concentrated at its centre. For any other figure, such as an oblate spheroid, this is not exactly true. A hollow concentric spherical sh.e.l.l exerts no force on small bodies inside it.

14. The earth's equatorial protuberance, being acted on by the attraction of the sun and moon, must disturb its axis of rotation in a calculated manner; and thus is produced the precession of the equinoxes.

[The attraction of the planets on the same protuberance causes a smaller and rather different kind of precession.]

15. The waters of the ocean are attracted towards the sun and moon on one side, and whirled a little further away than the solid earth on the other side: hence Newton explained all the main phenomena of the tides.

16. The sun's ma.s.s being known, he calculated the height of the solar tide.

17. From the observed heights of spring and neap tides he determined the lunar tide, and thence made an estimate of the ma.s.s of the moon.

REFERENCE TABLE OF NUMERICAL DATA.

+---------+---------------+----------------------+-----------------+ | |Ma.s.ses in Solar| Height dropped by a | Length of Day or| | | System. |stone in first second.|time of rotation.| +---------+---------------+----------------------+-----------------+ |Mercury | 065 | 70 feet | 24 hours | |Venus | 885 | 158 ” | 23-1/2 ” | |Earth | 1000 | 161 ” | 24 ” | |Mars | 108 | 62 ” | 24-1/2 ” | |Jupiter | 3008 | 450 ” | 10 ” | |Saturn | 897 | 184 ” | 10-1/2 ” | |The Sun | 316000 | 4360 ” | 608 ” | |The Moon | about 012 | 37 ” | 702 ” | +---------+---------------+----------------------+-----------------+

The ma.s.s of the earth, taken above as unity, is 6,000 trillion tons.

_Observatories._--Uraniburg flourished from 1576 to 1597; the Observatory of Paris was founded in 1667; Greenwich Observatory in 1675.

_Astronomers-Royal._--Flamsteed, Halley, Bradley, Bliss, Maskelyne, Pond, Airy, Christie.

LECTURE IX

NEWTON'S ”PRINCIPIA”

The law of gravitation, above enunciated, in conjunction with the laws of motion rehea.r.s.ed at the end of the preliminary notes of Lecture VII., now supersedes the laws of Kepler and includes them as special cases.

The more comprehensive law enables us to criticize Kepler's laws from a higher standpoint, to see how far they are exact and how far they are only approximations. They are, in fact, not precisely accurate, but the reason for every discrepancy now becomes abundantly clear, and can be worked out by the theory of gravitation.

We may treat Kepler's laws either as immediate consequences of the law of gravitation, or as the known facts upon which that law was founded.

Historically, the latter is the more natural plan, and it is thus that they are treated in the first three statements of the above notes; but each proposition may be worked inversely, and we might state them thus:--

1. The fact that the force acting on each planet is directed to the sun, necessitates the equable description of areas.

2. The fact that the force varies as the inverse square of the distance, necessitates motion in an ellipse, or some other conic section, with the sun in one focus.